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Homework Help: Checking method for calculating free charge from Electric field in LIH

  1. May 12, 2012 #1
    1. The problem statement, all variables and given/known data

    I'm asked to find the free charge per unit length on a cylinder which is surrounded by a LIH dielectric material. I have an expression for the electrostatic potential $$V(r)$$ in cylindrical coordinates.

    2. Relevant equations
    $$\mathbf{D}=\varepsilon \varepsilon_0 \mathbf{E}$$
    Gauss's Law in media equating flux of displacement field across a surface to the free charge.
    $$\mathbf{E}=-grad V$$

    3. The attempt at a solution
    I've calculated E using the last equation there, then used it (and the LIH assumption) to calculate D, and now I can equate:
    $$D_r \times 2 \pi r L = Q_f$$
    Where L is the length of the cylinder and Q_f is the free charge.
    This is enough to give me the expression for free charge per unit length. My problem is: am I right in taking the value of E at the cylinder surface?
    I know that the potential is zero on this surface, so that seems to throw my working out a little.
    Any advice appreciated.
  2. jcsd
  3. May 12, 2012 #2
    Why do you think the potential should be zero on the surface?
  4. May 12, 2012 #3
    I know that the potential is zero at the surface because I have the expression for V(r) and it works out as zero on the surface.

    I've just realised, though, that I could choose an arbitrary Gaussian surface in the dielectric and use that to calculate the free charge per unit length.

    Would that work?
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